Question

Use interval notation to indicate all real numbers between and including −4 and 7.

Answer 1

Answer:

[-4,7]

Step-by-step explanation:

square brackets [ ] mean including the number and parenthesis ( ) don't include the number. Also lowest number goes first and biggest number goes second.

Answer 2

Answer:

[-4, 7]

Step-by-step explanation:

the ‘( )’ implies not inclusive of, whereas ‘[ ]’ implies inclusive of

Therefore, that is the answer,

things to note in general:

- the values should go in ascending order from left to right

e.g (x, x+1) where x is a real number

- if you want to connect two intervals, you would use U or union

e.g (2, 3)U(4,5]

- also, from the previous answer, it is valid if you use set notation such as ‘(x, y]’ and ‘[x, y)’ where x < y, x and y are real

These are equivalent in ‘inequality notation’ as, if we consider p to be in these intervals:

x < p <= y

And

x <= p < y

respectively,

- If we have, say

(x,y]U[y,z) where x, y and z are real, x<y<z

You could combine it to form

(x,z)

Another example would be:

let p be in this domain

[x,x]

Which is equivalent to saying,

x<=p<=x

But by the squeeze theorem, we get that p = x

-notating asymptotes:

for asymptotes that graphs don’t exist beyond it, say, the range of y = e^x

it can be expressed as

(0, inf)

note that infinity is not, as I know of it, considered an asymptote, but we just can’t get to it exactly.

You can define infinity as, paraphrasing here ‘the number of numbers’

we actually can’t assign a value to that, as there will be a number at least 1 greater than any number you specify, but I digress,

The asymptote here is really y = 0 as when x is negative, we can reciprocate to get a fraction, which has 1 in the numerator.

But we all know that a fraction with a constant numerator cannot equal 0 for any denominator in the set of real numbers

Therefore, the asymptote is y = 0

Applying the same logic,

for asymptotes that graphs do exist beyond them, say, y = 1/x

The range is

(-inf, 0)U(0, inf)

where the asymptote is again y = 0